With two identical lightbulbs and two identical batteries, how would you arrange the bulbs and batteries in a circuit to get the maximum possible total power out? (Assume the batteries have negligible internal resistance.)

A single resistor dissipates 8 watts of power when connected directly across a battery. If a second identical resistor is added in series with the first, what power will the original resistor dissipate?

Consider the two circuits depicted in Figure 19.81. In circuit 1, ohmic resistor $R_1$ dissipates 5 W; in circuit 2, ohmic resistor $R_2$ dissipates 20 W. The wires and batteries have negligible resistance. The circuits contain 10 V batteries. What is the resistance of $R_1$ and of $R_2$ ?

Resistor $R_1$ is made of a very thin metal wire that is 3 mm long, with a diameter of 0.1 mm. What is the electric field inside this metal resistor?

(b) A thin copper wire in this circuit is 5 mm long and has a constant cross section of $0.2 \mathrm{mm}^{2}$ . The conductivity of copper at room temperature is $\sigma=6 \times 10^{7} \mathrm{ohm}^{-1} \mathrm{m}^{-1}$ . The copper wire is in series with the carbon resistor, with one end connected to the 15 V end of the carbon resistor, and the current you calculated in part (a) runs through the carbon resistor wire. Calculate the resistance R of the copper wire and the potential Vat end at the other end of the wire. You can see that for most purposes a thick copper wire in a circuit would have practically a uniform potential. This is because the small drift speed in a thick, high-conductivity copper wire requires only a very small electric field, and the integral of this very small field creates a very small potential difference along the wire

A carbon resistor is 5 mm long and has a constant cross section of $0.2 \mathrm{mm}^{2}$ . The conductivity of carbon at room temperature is $\sigma=3 \times 10^{4}$ per ohm.m. In a circuit its potential at one end of the resistor is 12 V relative to ground, and at the other end the potential is 15 V. Calculate the resistance R and the current I.

A net charge of 45 mC passes through the cross-sectional area of a wire in 15 s. How many electrons pass the cross-sectional area in 1.0 min?

n gold at room temperature, the mobility of mobile electrons is about $4.3 \times 10^{-3}(\mathrm{m} / \mathrm{s}) /(\mathrm{V} / \mathrm{m}),$ and there are about $5.9 \times 10^{28}$ mobile electrons per cubic meter. Calculate the conductivity of gold, including correct units.

Suppose that you charged a 2.5 F capacitor with two 1.5 V batteries. How much charge would be on each plate in the final state? How many excess electrons would be on the negative plate?

Two circular plates of radius 0.12 m are separated by an air gap of 1.5 mm. The plates carry charge +Q and -Q where $Q=3.6 \times 10^{-8}\ \mathrm{C}.$ What is the capacitance of this capacitor?

Two circular plates of radius 0.12 m are separated by an air gap of 1.5 mm. The plates carry charge +Q and -Q where $Q=3.6 \times 10^{-8}\ \mathrm{C}.$ What is the magnitude of the electric field in the gap?

A certain 6 V battery delivers 12 A when short-circuited. How much current does the battery deliver when a $1\ \Omega$ resistor is connected to it?

Three $45~\Omega$ lightbulbs and three $65~\Omega$ lightbulbs are connected in series. What is the total resistance if all six are wired in parallel?

A three-way lightbulb can produce 50 W, 100 W, or 150 W, at 120 V. Such a bulb contains two filaments that can be connected to the 120 V individually or in parallel. Describe how the connections to the two filaments are made to give each of the three wattages. What must be the resistance of each filament?